Question: Simplify the following expression: $x = \dfrac{q^2 - q - 2}{q + 1} $
Explanation: First factor the polynomial in the numerator. $ q^2 - q - 2 = (q + 1)(q - 2) $ So we can rewrite the expression as: $x = \dfrac{(q + 1)(q - 2)}{q + 1} $ We can divide the numerator and denominator by $(q + 1)$ on condition that $q \neq -1$ Therefore $x = q - 2; q \neq -1$